Recommender systems are an important component of many websites. Two of the most popular approaches are based on matrix factorization (MF) and Markov chains (MC). MF methods learn the general taste of a user by factorizing the matrix over observed user-item preferences. On the other hand, MC methods model sequential behavior by learning a transition graph over items that is used to predict the next action based on the recent actions of a user. In this paper, we present a method bringing both approaches together. Our method is based on personalized transition graphs over underlying Markov chains. That means for each user an own transition matrix is learned -thus in total the method uses a transition cube. As the observations for estimating the transitions are usually very limited, our method factorizes the transition cube with a pairwise interaction model which is a special case of the Tucker Decomposition. We show that our factorized personalized MC (FPMC) model subsumes both a common Markov chain and the normal matrix factorization model. For learning the model parameters, we introduce an adaption of the Bayesian Personalized Ranking (BPR) framework for sequential basket data. Empirically, we show that our FPMC model outperforms both the common matrix factorization and the unpersonalized MC model both learned with and without factorization.

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The situation in which a choice is made is an important information for recommender systems. Context-aware recommenders take this information into account to make predictions. So far, the best performing method for contextaware rating prediction in terms of predictive accuracy is Multiverse Recommendation based on the Tucker tensor factorization model. However this method has two drawbacks:(1) its model complexity is exponential in the number of context variables and polynomial in the size of the factorization and (2) it only works for categorical context variables. On the other hand there is a large variety of fast but specialized recommender methods which lack the generality of contextaware methods.We propose to apply Factorization Machines (FMs) to model contextual information and to provide context-aware rating predictions. This approach results in fast contextaware recommendations because the model equation of FMs can be computed in linear time both in the number of context variables and the factorization size. For learning FMs, we develop an iterative optimization method that analytically finds the least-square solution for one parameter given the other ones. Finally, we show empirically that our approach outperforms Multiverse Recommendation in prediction quality and runtime.

Abstract-Cold-start scenarios in recommender systems are situations in which no prior events, like ratings or clicks, are known for certain users or items. To compute predictions in such cases, additional information about users (user attributes, e.g. gender, age, geographical location, occupation) and items (item attributes, e.g. genres, product categories, keywords) must be used.We describe a method that maps such entity (e.g. user or item) attributes to the latent features of a matrix (or higherdimensional) factorization model. With such mappings, the factors of a MF model trained by standard techniques can be applied to the new-user and the new-item problem, while retaining its advantages, in particular speed and predictive accuracy.We use the mapping concept to construct an attributeaware matrix factorization model for item recommendation from implicit, positive-only feedback. Experiments on the newitem problem show that this approach provides good predictive accuracy, while the prediction time only grows by a constant factor.

A key element of the social networks on the internet such as Facebook and Flickr is that they encourage users to create connections between themselves, other users and objects.One important task that has been approached in the literature that deals with such data is to use social graphs to predict user behavior (e.g. joining a group of interest). More specifically, we study the cold-start problem, where users only participate in some relations, which we will call social relations, but not in the relation on which the predictions are made, which we will refer to as target relations.We propose a formalization of the problem and a principled approach to it based on multi-relational factorization techniques. Furthermore, we derive a principled feature extraction scheme from the social data to extract predictors for a classifier on the target relation. Experiments conducted on real world datasets show that our approach outperforms current methods.